Title: On the rationality of moduli spaces of pointed curves
Abstract:Motivated by several recent results on the geometry of the moduli spaces M ¯ g , n of stable curves of genus g with n marked points, we determine the birational structure of these spaces for small val...Motivated by several recent results on the geometry of the moduli spaces M ¯ g , n of stable curves of genus g with n marked points, we determine the birational structure of these spaces for small values of g and n by exploiting suitable plane models of a general curve. More precisely, ℳg,n is shown to be rational for g = 2 and 1 ⩽ n ⩽ 12, g = 3 and 1 ⩽ n ⩽ 14, g = 4 and 1 ⩽ n ⩽ 15, and g = 5 and 1 ⩽ n ⩽ 12Read More